In processing leather it is necessary to ensure, before carrying out certain operations, that the moisture content of the leather is within the preferred range. Accordingly it has previously been proposed to introduce moisture into leather using a suitable apparatus. One known apparatus for moistening and conditioning leather is described in U.K. patent specification No. 1,288,735 (Statni Vyzkumny Ustav Kozedelny). The apparatus described in this British patent specification comprises heater rolls of relatively large diameter and two conveyor belts between which the leather is transported, the belts being guided on an S-shape path round the heater rolls. This known apparatus further comprises guiding rollers disposed before and after the heater rolls, which ensure that the conveyor belts are brought together prior to reaching the heater rolls and are separated again after they have passed the heater rolls. At the input side of the conveyor belts (that is before the belts reach the heater rolls as they travel along), the conveyor belts are moistened. By reason of the S-shaped course of the conveyor belts round the heater rolls a number of guiding rollers are necessary, thus incurring considerable expense. Furthermore alignment of the conveyor belt is difficult in the event that it is necessary to replace one or both of the belts. In addition it is impossible to use endless belts when replacing the belts: after the belts have been aligned in the apparatus, they must be connected, and this gives rise to a region at the connecting point where the capacity of the belt to take up water is different from that of the remainder of the belt. This causes a corresponding change in the degree of moistening of the leather at the region where the leather is transported in contact with the connecting region of the conveyor belt. In this known apparatus the duration of moistening depends upon the speed of the conveyor belt and thus the throughput of the apparatus is dependent upon the duration of moistening required. The duration of moistening should be adjusted in accordance with the type of leather to be operated upon, so that when a change occurs in the type of leather to be operated upon the known apparatus must operate at a different throughput speed.